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Comparing Lines' Gradients

Comparing Lines' Gradients
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2017-12-22 22:11
FunctionCoordinate GeometryDerivativeGeometric ConstructionSlider Animation
In collections Mathematics Form 2
This example demonstrates how to compare the gradients of different lines. The core math concepts involved include slope, coordinate geometry, and function graphing. Key GeoGebra commands used in construction are If, DynamicCoordinates, Line, Slope, Segment, SelectedIndex, etc., for creating and manipulating points, lines, and text objects. Suitable for high school students learning coordinate geometry and functions.

GeoGebra Commands & Parameters

  1. If(y(B) > y(O), 1, y(B) ≟ y(O), 0, -1) → r
  2. If(Distance[B, Q_1] < 0.1, Q_1, Distance[B, Q_2] < 0.1, Q_2, Distance[B, Q_3] < 0.1, Q_3, B) → D
  3. If(Distance[B, P_1] < 0.1, P_1, Distance[B, P_2] < 0.1, P_2, Distance[B, P_3] < 0.1, P_3, B) → C
  4. DynamicCoordinates(B, If[r ≟ 1, x(C), x(D)], If[r ≟ 1, y(C), y(D)]) → A
  5. Line(O, A) → f
  6. Slope(f) → a
  7. Line(O, P_1) → g
  8. Line(O, P_2) → h
  9. Line(O, P_3) → i
  10. Slope(g) → OP01
  11. Slope(h) → OP02
  12. Slope(i) → OP03
  13. Segment(O, P_1) → j
  14. Segment(O, P_2) → k
  15. Segment(O, P_3) → l
  16. SelectedIndex(Bahasa) → n
  17. If(n ≟ 1, If[r ≟ 1, "Lines sloping up", r ≟ -1, "Lines sloping down"], If[r ≟ 1, "Garis condong ke atas", r ≟ -1, "Garis condong ke bawah"]) → Text2
  18. If(n ≟ 1, "Gradient of OA = " + (Text[a]), "Kecerunan OA = " + (Text[a])) → Text1
  19. If(n ≟ 1, "Gradient of ", "Kecerunan ") → Tex1
  20. Line(O, Q_1) → m
  21. Line(O, Q_2) → s
  22. Line(O, Q_3) → t
  23. Slope(m) → OQ01
  24. Slope(s) → OQ02
  25. Slope(t) → OQ03
  26. Segment(O, Q_1) → b
  27. Segment(O, Q_2) → c
  28. Segment(O, Q_3) → d